Finite Group Databasebeta

← C2×C3×#4949 #11808475

Subgroups — C2×C3×#4949 #11808475

Order 1152.

2153 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C22⋊C4C211yesmaximal, characteristic
2C22×C3×#217C212yesmaximal
3C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C22×C3×Dic3⋊C4C212yesmaximal, complemented
5C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
6C3×#4949C218yesmaximal, direct product factor
7C2×C3×#399—31nomaximal
8C2×#4949C311yesmaximal, characteristic, direct product factor
9C25×C32C2211yescharacteristic
10C23×C32×C4C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C23×C3×Dic3C2212yes—
13C23×C3×Dic3C2212yes—
14C2×C32×C22⋊C4—24no—
15C2×C32×C22⋊C4C2214yes—
16C2×C3×#217—28no—
17C2×C3×#217C2218yes—
18C2×C3×C4⋊Dic3—24no—
19C2×C3×C4⋊Dic3C2214yescomplemented
20C2×C3×Dic3⋊C4—28no—
21C2×C3×Dic3⋊C4C2218yescomplemented
22C3×C3⋊#95C2214yescomplemented
23C22×C3×C4⋊C4—32no—
24C22×C3×C4⋊C4—31no—
25C22×C3×C22⋊C4—21no—
26C22×C3×C22⋊C4—32no—
27C22×C3×C22⋊C4D311yescharacteristic
28C22×C3×C22⋊C4C2×C311yescharacteristic
29C22×#217C2×C312yes—
30C22×C4⋊Dic3C2×C311yescharacteristic, complemented
31C22×Dic3⋊C4C2×C312yescomplemented
32C3×#399—38no—
33C2×C3×#95—31no—
34C2×C3⋊#95C2×C311yescharacteristic, complemented
35#4949C2×C318yesdirect product factor
36C24×C32—22no—
37C24×C32—24no—
38C24×C32—22no—
39C24×C32—24no—
40C24×C32Q814yes—
41C24×C32C2312yes—
42C24×C32C2311yescharacteristic
43C22×C32×C4—24no—
44C22×C32×C4—22no—
45C22×C32×C4—24no—
46C22×C32×C4D414yes—
47C22×C32×C4C2312yes—
48C22×C32×C4C2312yes—
49C22×C3×Dic3—24no—
50C22×C3×Dic3—24no—
51C22×C3×Dic3—24no—
52C22×C3×Dic3—24no—
53C22×C3×Dic3—24no—
54C22×C3×Dic3D418yes—
55C22×C3×Dic3C2314yes—
56C22×C3×Dic3C2314yes—
57C32×C22⋊C4—28no—
58C3×#217—216no—
59C3×C4⋊Dic3—28no—
60C3×Dic3⋊C4—216no—
61C2×#399—31noSylow
62C25×C3—21no—
63C25×C3C2×D311yescharacteristic
64C25×C3C22×C311yescharacteristic
65C23×C3×C4—21no—
66C23×C3×C4—21no—
67C23×C3×C4—32no—
68C23×C3×C4—32no—
69C23×C3×C4C2×D311yescharacteristic
70C23×C3×C4C2×D311yescharacteristic
71C23×C3×C4C22×C311yescharacteristic
72C23×C3×C4C22×C311yescharacteristic
73C23×Dic3C22×C312yes—
74C23×Dic3C22×C312yes—
75C2×C3×C4⋊C4—38no—
76C2×C3×C4⋊C4—34no—
77C2×C3×C4⋊C4—68no—
78C2×C3×C4⋊C4—64no—
79C2×C3×C22⋊C4—28no—
80C2×C3×C22⋊C4—24no—
81C2×C3×C22⋊C4—24no—
82C2×C3×C22⋊C4—24no—
83C2×C3×C22⋊C4—38no—
84C2×C3×C22⋊C4—68no—
85C2×C3×C22⋊C4C2×D314yes—
86C2×C3×C22⋊C4C22×C314yes—
87C2×#217—28no—
88C2×#217C22×C318yes—
89C2×C4⋊Dic3—24no—
90C2×C4⋊Dic3C22×C314yescomplemented
91C2×Dic3⋊C4—28no—
92C2×Dic3⋊C4C22×C318yescomplemented
93C3×#95—34no—
94C3⋊#95C22×C314yescomplemented
95C23×C32—28no—
96C23×C32—22no—
97C23×C32—22no—
98C23×C32—216no—
99C23×C32—24no—
100C23×C32—24no—
101C23×C32—48no—
102C23×C32—44no—
103C23×C32—44no—
104C23×C32C2×D414yes—
105C23×C32C2×D412yes—
106C23×C32C2×Q814yes—
107C23×C32C2×Q812yes—
108C23×C32#4112yes—
109C23×C32#4114yes—
110C23×C32C2411yescharacteristic
111C2×C32×C4—22no—
112C2×C32×C4—28no—
113C2×C32×C4—24no—
114C2×C32×C4—24no—
115C2×C32×C4—44no—
116C2×C32×C4C2×D414yes—
117C2×C3×Dic3—216no—
118C2×C3×Dic3—24no—
119C2×C3×Dic3—24no—
120C2×C3×Dic3—24no—
121C2×C3×Dic3—24no—
122C2×C3×Dic3—24no—
123C2×C3×Dic3—48no—
124C2×C3×Dic3C2×D418yes—
125C22×C4⋊C4—32no—
126C22×C4⋊C4—31no—
127C22×C22⋊C4—32no—
128C22×C22⋊C4C3×D311yescharacteristic
129#399—38no—
130C2×#95—31no—
131C24×C3—24no—
132C24×C3—24no—
133C24×C3—22no—
134C24×C3—24no—
135C24×C3—24no—
136C24×C3—22no—
137C24×C3—24no—
138C24×C3—22no—
139C24×C3—22no—
140C24×C3—24no—
141C24×C3—24no—
142C24×C3—21no—
143C24×C3—22no—
144C24×C3—44no—
145C24×C3—44no—
146C24×C3Dic614yes—
147C24×C3C3×Q814yes—
148C24×C3C22×D312yes—
149C24×C3C22×D311yescharacteristic
150C24×C3C23×C312yes—
151C24×C3C23×C311yescharacteristic
152C22×C3×C4—24no—
153C22×C3×C4—24no—
154C22×C3×C4—24no—
155C22×C3×C4—24no—
156C22×C3×C4—22no—
157C22×C3×C4—24no—
158C22×C3×C4—22no—
159C22×C3×C4—24no—
160C22×C3×C4—22no—
161C22×C3×C4—22no—
162C22×C3×C4—38no—
163C22×C3×C4—34no—
164C22×C3×C4—34no—
165C22×C3×C4—44no—
166C22×C3×C4—44no—
167C22×C3×C4—64no—
168C22×C3×C4—64no—
169C22×C3×C4—64no—
170C22×C3×C4—64no—
171C22×C3×C4—64no—
172C22×C3×C4#6714yes—
173C22×C3×C4C3×D414yes—
174C22×C3×C4C22×D312yes—
175C22×C3×C4C22×D312yes—
176C22×C3×C4C23×C312yes—
177C22×C3×C4C23×C312yes—
178C22×Dic3—24no—
179C22×Dic3—24no—
180C22×Dic3—24no—
181C22×Dic3—24no—
182C22×Dic3—24no—
183C22×Dic3C3×D418yes—
184C22×Dic3C23×C314yes—
185C22×Dic3C23×C314yes—
186C3×C4⋊C4—616no—
187C3×C4⋊C4—68no—
188C3×C22⋊C4—216no—
189C3×C22⋊C4—28no—
190C3×C22⋊C4—28no—
191C3×C22⋊C4—616no—
192#217—216no—
193C4⋊Dic3—28no—
194Dic3⋊C4—216no—
195C22×C32—24no—
196C22×C32—28no—
197C22×C32—44no—
198C22×C32—42no—
199C22×C32—42no—
200C22×C32—416no—
201C22×C32C22⋊Q818yes—
202C22×C32C22⋊Q814yes—
203C22×C32#12318yes—
204C22×C32#12314yes—
205C22×C32#12714yes—
206C22×C32C22×D412yes—
207C22×C32C22×D411yescharacteristic
208C22×C32C22×Q811yescharacteristic
209C22×C32C2×#4111yescharacteristic
210C22×C32C2×#4112yes—
211C32×C4—24no—
212C32×C4—42no—
213C3×Dic3—28no—
214C3×Dic3—44no—
215C25C2×C3×D311yescharacteristic
216C23×C4—32no—
217C23×C4—32no—
218C23×C4C2×C3×D311yescharacteristic
219C23×C4C2×C3×D311yescharacteristic
220C2×C4⋊C4—38no—
221C2×C4⋊C4—34no—
222C2×C4⋊C4—68no—
223C2×C4⋊C4—64no—
224C2×C22⋊C4—24no—
225C2×C22⋊C4—38no—
226C2×C22⋊C4—68no—
227C2×C22⋊C4C2×C3×D314yes—
228#95—34no—
229C23×C3—24no—
230C23×C3—216no—
231C23×C3—24no—
232C23×C3—216no—
233C23×C3—28no—
234C23×C3—216no—
235C23×C3—28no—
236C23×C3—22no—
237C23×C3—24no—
238C23×C3—24no—
239C23×C3—22no—
240C23×C3—24no—
241C23×C3—22no—
242C23×C3—22no—
243C23×C3—24no—
244C23×C3—21no—
245C23×C3—22no—
246C23×C3—24no—
247C23×C3—22no—
248C23×C3—24no—
249C23×C3—24no—
250C23×C3—22no—
251C23×C3—416no—
252C23×C3—44no—
253C23×C3—44no—
254C23×C3—416no—
255C23×C3—48no—
256C23×C3—48no—
257C23×C3—48no—
258C23×C3—44no—
259C23×C3—44no—
260C23×C3—48no—
261C23×C3—44no—
262C23×C3—44no—
263C23×C3C2×Dic614yes—
264C23×C3C2×Dic612yes—
265C23×C3#23512yes—
266C23×C3D3×D414yes—
267C23×C3#23714yes—
268C23×C3C2×#6712yes—
269C23×C3C2×C3×D414yes—
270C23×C3C2×C3×D412yes—
271C23×C3C2×C3×Q814yes—
272C23×C3C2×C3×Q812yes—
273C23×C3C3×#4112yes—
274C23×C3C3×#4114yes—
275C23×C3C23×D311yescharacteristic
276C23×C3C24×C311yescharacteristic
277C2×C3×C4—28no—
278C2×C3×C4—28no—
279C2×C3×C4—24no—
280C2×C3×C4—24no—
281C2×C3×C4—24no—
282C2×C3×C4—24no—
283C2×C3×C4—22no—
284C2×C3×C4—24no—
285C2×C3×C4—22no—
286C2×C3×C4—24no—
287C2×C3×C4—38no—
288C2×C3×C4—48no—
289C2×C3×C4—44no—
290C2×C3×C4—44no—
291C2×C3×C4—48no—
292C2×C3×C4—44no—
293C2×C3×C4—44no—
294C2×C3×C4—616no—
295C2×C3×C4—64no—
296C2×C3×C4—64no—
297C2×C3×C4—64no—
298C2×C3×C4—64no—
299C2×C3×C4—64no—
300C2×C3×C4—128no—
301C2×C3×C4C2×#6714yes—
302C2×C3×C4C2×C3×D414yes—
303C2×Dic3—216no—
304C2×Dic3—24no—
305C2×Dic3—24no—
306C2×Dic3—24no—
307C2×Dic3—24no—
308C2×Dic3—24no—
309C2×Dic3—48no—
310C2×Dic3C2×C3×D418yes—
311C2×C32—44no—
312C2×C32#39918yescomplemented
313C2×C32C2×C22⋊Q812yes—
314C2×C32C2×C22⋊Q811yescharacteristic
315C2×C32C2×#12312yes—
316C2×C32C2×#12311yescharacteristic
317C2×C32C2×#12711yescharacteristic
318C24—22no—
319C24—24no—
320C24—24no—
321C24—22no—
322C24C3×Dic614yes—
323C24C22×C3×D312yes—
324C24C22×C3×D311yescharacteristic
325C22×C4—24no—
326C22×C4—24no—
327C22×C4—22no—
328C22×C4—34no—
329C22×C4—38no—
330C22×C4—34no—
331C22×C4—64no—
332C22×C4—64no—
333C22×C4—64no—
334C22×C4—64no—
335C22×C4—64no—
336C22×C4C3×#6714yes—
337C22×C4C22×C3×D312yes—
338C22×C4C22×C3×D312yes—
339C4⋊C4—616no—
340C4⋊C4—68no—
341C22⋊C4—28no—
342C22⋊C4—616no—
343C22×C3—28no—
344C22×C3—28no—
345C22×C3—24no—
346C22×C3—24no—
347C22×C3—28no—
348C22×C3—28no—
349C22×C3—28no—
350C22×C3—24no—
351C22×C3—24no—
352C22×C3—24no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—22no—
356C22×C3—22no—
357C22×C3—21no—
358C22×C3—48no—
359C22×C3—48no—
360C22×C3—432no—
361C22×C3—44no—
362C22×C3—44no—
363C22×C3—416no—
364C22×C3—44no—
365C22×C3—416no—
366C22×C3—42no—
367C22×C3—42no—
368C22×C3—44no—
369C22×C3—42no—
370C22×C3—42no—
371C22×C3#87818yes—
372C22×C3#88318yes—
373C22×C3#92414yes—
374C22×C3#93514yes—
375C22×C3#94014yes—
376C22×C3C3×C22⋊Q818yes—
377C22×C3C3×C22⋊Q814yes—
378C22×C3C3×#12318yes—
379C22×C3C3×#12314yes—
380C22×C3C3×#12714yes—
381C22×C3C22×Dic611yescharacteristic
382C22×C3C2×#23511yescharacteristic
383C22×C3C2×D3×D412yes—
384C22×C3C2×#23712yes—
385C22×C3C22×#6711yescharacteristic
386C22×C3C22×C3×D412yes—
387C22×C3C22×C3×D411yescharacteristic
388C22×C3C22×C3×Q811yescharacteristic
389C22×C3C2×C3×#4111yescharacteristic
390C22×C3C2×C3×#4112yes—
391C3×C4—24no—
392C3×C4—24no—
393C3×C4—44no—
394C3×C4—44no—
395C3×C4—42no—
396C3×C4—42no—
397C3×C4—68no—
398C3×C4—124no—
399Dic3—28no—
400Dic3—44no—
401C32C2×#39911yescharacteristic, complemented, Sylow
402C23—216no—
403C23—28no—
404C23—22no—
405C23—24no—
406C23—24no—
407C23—22no—
408C23—48no—
409C23—44no—
410C23—44no—
411C23C2×C3×Dic614yes—
412C23C2×C3×Dic612yes—
413C23C3×#23512yes—
414C23C3×D3×D414yes—
415C23C3×#23714yes—
416C23C2×C3×#6712yes—
417C23C23×C3×D311yescharacteristic
418C2×C4—28no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—22no—
422C2×C4—38no—
423C2×C4—44no—
424C2×C4—616no—
425C2×C4—64no—
426C2×C4—64no—
427C2×C4—64no—
428C2×C4—64no—
429C2×C4—64no—
430C2×C4—128no—
431C2×C4C2×C3×#6714yes—
432C2×C3—22no—
433C2×C3—21no—
434C2×C3—28no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—22no—
438C2×C3—48no—
439C2×C3—44no—
440C2×C3—44no—
441C2×C3#494918yesdirect product factor
442C2×C3C3×#39918yescomplemented
443C2×C3C2×#87812yes—
444C2×C3C2×#88312yes—
445C2×C3C2×#92411yescharacteristic
446C2×C3C2×#93511yescharacteristic
447C2×C3C2×#94011yescharacteristic
448C2×C3C2×C3×C22⋊Q811yescharacteristic
449C2×C3C2×C3×C22⋊Q812yes—
450C2×C3C2×C3×#12312yes—
451C2×C3C2×C3×#12311yescharacteristic
452C2×C3C2×C3×#12711yescharacteristic
453C22—24no—
454C22—28no—
455C22—44no—
456C22—416no—
457C22—42no—
458C22—42no—
459C22C3×#87818yes—
460C22C3×#88318yes—
461C22C3×#92414yes—
462C22C3×#93514yes—
463C22C3×#94014yes—
464C22C22×C3×Dic611yescharacteristic
465C22C2×C3×#23511yescharacteristic
466C22C2×C3×D3×D412yes—
467C22C2×C3×#23712yes—
468C22C22×C3×#6711yescharacteristic
469C4—24no—
470C4—42no—
471C4—68no—
472C4—124no—
473C3—21no—
474C3C2×#494911yescharacteristic, direct product factor
475C3C2×C3×#39911yescharacteristic, complemented
476C2—44no—
477C2C3×#494918yesdirect product factor
478C2C2×C3×#87812yes—
479C2C2×C3×#88312yes—
480C2C2×C3×#92411yescharacteristic
481C2C2×C3×#93511yescharacteristic
482C2C2×C3×#94011yescharacteristic
subgroupG/H
centerC24×C3C22×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC22×C32×C22⋊C4C2
socleC24×C32C23
prime radicalC25×C32C22
hypercenterC22×C3×C22⋊C4D3
hypocenterC3C2×C3×#399
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C22×C3×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C22×C3×C4⋊Dic3C2semidirect
4. C22×C3×Dic3⋊C4C2semidirect
5. C2×C3×C3⋊#95C2semidirect
6. C3×#4949C2direct (N × H)
8. C2×#4949C3direct (N × H)
19. C2×C3×C4⋊Dic3C22semidirect
21. C2×C3×Dic3⋊C4C22semidirect
22. C3×C3⋊#95C22semidirect
30. C22×C4⋊Dic3C2×C3semidirect
31. C22×Dic3⋊C4C2×C3semidirect
34. C2×C3⋊#95C2×C3semidirect
35. #4949C2×C3direct (N × H)
90. C2×C4⋊Dic3C22×C3semidirect
92. C2×Dic3⋊C4C22×C3semidirect
94. C3⋊#95C22×C3semidirect
312. C2×C32#399semidirect
401. C32C2×#399semidirect
441. C2×C3#4949direct (N × H)
442. C2×C3C3×#399semidirect
474. C3C2×#4949direct (N × H)
475. C3C2×C3×#399semidirect
477. C2C3×#4949direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C32×C22⋊C42
C22×C3×#2172
C22×C3×C4⋊Dic32
C22×C3×Dic3⋊C42
C2×C3×C3⋊#952
C3×#49492
C2×C3×#3993
C2×#49493